Rate-dependent plastic flow

Wallace [15], [16] gives details on effects of nonlinear material behavior and compression-induced anisotropy in initially isotropic materials for weak shocks, and Johnson et ai. [17] give results for infinitesimal compression of initially anisotropic single crystals, but the forms of the equations are the same as for (7.10)-(7.11). From these results it is easy to see where the micromechanical effects of rate-dependent plastic flow are included in the analysis the micromechanics (through the mesoscale variables and n) is contained in the term y, as given by (7.1). 

Metals Successful applications of metals in high-temperature process service depend on an appreciation of certain engineering factors. The important alloys for service up to I,I00°C (2,000°F) are shown in Table 28-35. Among the most important properties are creep, rupture, and short-time strengths (see Figs. 28-23 and 28-24). Creep relates initially applied stress to rate of plastic flow. Stress... 

An example of research in the micromechanics of shock compression of solids is the study of rate-dependent plasticity and its relationship to crystal structure, crystal orientation, and the fundamental unit of plasticity, the dislocation. The majority of data on high-rate plastic flow in shock-compressed solids is in the form of ... 

Solids 12, 59 - 65 (1964) "A Generalized Theory of Strain- Rate- Dependent Plastic Wave Propagation in Bars 86) M. Lutzky, "The Flow Field Behind a Spherical Detonation in TNT, Using the Landau- Stanyukovich Equation, USNOL-White Oak, NOLTR 64-40 Dec 1964)... 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

Strength and Stiffness. Thermoplastic materials are viscoelastic which means that their mechanical properties reflect the characteristics of both viscous liquids and elastic solids. Thus when a thermoplastic is stressed it responds by exhibiting viscous flow (which dissipates energy) and by elastic displacement (which stores energy). The properties of viscoelastic materials are time, temperature and strain rate dependent. Nevertheless the conventional stress-strain test is frequently used to describe the (short-term) mechanical properties of plastics. It must be remembered, however, that as described in detail in Chapter 2 the information obtained from such tests may only be used for an initial sorting of materials. It is not suitable, or intended, to provide design data which must usually be obtained from long term tests. 

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, they are categorized into pseudoplastic, dilatant, and Bingham plastic fluids (Figure 2.2). The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is applied, after which the shear stress increases linearly with the shear rate. In general, the shear stress r can be represented by Equation 2.6 ... 

The plastic flow of compounded stock of rubber is dependent upon the temperature, force and the rate of force. Obviously these three variables are significant in measuring the processibility of rubber or its compound. After forming the stock to the desired shape, the compounds need to be converted into a strong elastic material. This is... 

Depending on the material and deformation conditions (strain rate, temperature) other stress-strain curve shapes can be observed (Fig. 2b and c). In Fig. 2b, the plastic flow occurs at the same stress level as that required for the yielding so the strain softening does not exist. In the case shown in Fig. 2c, the strain hardening happens very close to yielding, suppressing both strain softening and plastic flow behaviour. 

Fig. 14 Temperature dependence of yield stress, cry, and plastic flow stress, crpf, for quenched and physically aged PMMA. Strain rate is 2 x 10-3 s-1 (From [32])...

The strain rate dependence of the plastic flow, crpf, is shown at various temperatures in Fig. 20. It is clear that crpf is lightly dependent on the strain rate,... 

Fig. 20 Strain rate dependence of yield stress, ay, and plastic flow stress, apf, of PMMA at the indicated temperatures (From [33])...

In the model leading to Eq. 1 and Eq. 2, not only the elastic and plastic flow properties, but also Of must also be assumed to be time-dependent for the results to be consistent with experimental data obtained at different crack growth rates [52]. To illustrate the consequences of this, the time-dependence is grouped together in a single power law term, so that Eq. 1 becomes ... 

Chlorine gas is generated when chlorine bleach is mixed with sodium bisulfate (Sani-Flush). Pour a can of Sani-Flush in a baking pan, and level off the top of the pile. Punch a hole near Che bottom of the plastic bleach jug and place the jug in the center of the pan. A steady cloud of gas will be generated, the actual duration depending upon the rate of bleach flow. If It is necessary to direct the gas to a specific area, the generator can be covered with an airtight top fitted with a... 

For T < Tg, the viscoplastic model used here accounts for intrinsic softening upon yielding followed by progressive orientational hardening. Rate dependent flow is taken to be governed by Argon s formulation [5] of the equivalent plastic strain rate... 

David and Augsburger (63) studied the decay of compressional forces for a variety of excipients, compressed with flat-faced punches on a Stokes rotary press. They found that initial compressive force could be subject to a fairly rapid decay and that this rate was dependent on the deformation behavior of the excipient for the materials studied, they found that maximum loss in compression force was for compressible starch and MCC, which was followed by compressible sugar and DCP. This was attributed to differences in the extent of plastic flow. The decay curves were analyzed using the Maxwell model of viscoelastic behavior. Maxwell model implies first order decay of compression force. 

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